Cisco aptitude questions

1 What is the probability of getting at least one six in a single throw of three unbiased dice?

(1) 1 / 6
(2) 125 / 216
(3) 1 / 36
(4) 81 / 216
(5) 91 / 216

Correct choice is (5) and Correct Answer is 91 / 216
Explanatory Answer
Every die has got six sides. Each of the sides is numbered from 1 to 6.
When a single unbiased die is thrown you can have six possible outcomes.
When two dice are thrown simultaneously, the total number of outcomes will be 6 * 6 = 36
Similarly, when three dice are thrown simultaneously, the total number of outcomes will be 6*6*6=216.
We need to find out the number of cases in which at least one of the facing sides shows 6.
At least one means - either one dice or two dice or all three.

Case 1: Let us take the easiest case first - all three dice showing '6' - There is only one such possibility.

Case 2: The number of cases in which two of the dice show 6 and one of them is a different number.
For eg an event like 6 6 5 will be one of the outcomes for case 2.

As two of the dice show '6' , it can happen in only one way. The third die shows a different number, a number other than 6, and it can be any of the 5 other numbers. Therefore, there will 5 possible options i.e. (1, 6, 6), (2, 6, 6), (3, 6, 6), (4, 6, 6), (5, 6, 6).

However, each of these possibilities can have three different arrangements depending upon where the third different digit appears. For example take (1, 6, 6) case - it will have three options (1, 6, 6), (6, 1, 6), (6, 6, 1).

Therefore, the total number of events in which 2 of the dice will show '6' and one will show a different number = 5*3 = 15 cases.

Case 3: When only one of the die shows '6' and the other two show numbers other than '6'.

The die showing '6' has only one option. The other two dice can have any of the '5' options. Therefore, the total number of possibilities = 1*5*5 = 25.

However, the die showing '6' can either be the first die or the second die or the third die.

3 The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?
Rs 570
Rs 420
Rs 690
Rs 640
Rs 610
Correct Answer - Rs 420. Choice (2)

When a new manager joins, the new average salary drops to Rs.580 for the total team of 15 of them.

The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager = 580 *15 = 8700

Therefore, the salary of the new manager is 9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420.

An alternative method of doing the problem is as follows:

The average salary dropped by Rs.20 for 15 of them. Therefore, the overall salary has dropped by 15*20 = 300.

Therefore, the new manager's salary should be Rs.300 less than that of the old manager = 720 - 300 = 420.

Correct answer choice (2)

4 If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

(1) 24
(2) 31
(3) 32
(4) 30Correct Answer - (3)
Solution:

The 5 letter word can be rearranged in 5! Ways = 120 without any of the letters repeating.

The first 24 of these words will start with A.

Then the 25th word will start will CA _ _ _. The remaining 3 letters can be rearranged in 3! Ways = 6. i.e. 6 words exist that start with CA.

The next word starts with CH and then A, i.e., CHA _ _. The first of the words will be CHAMS. The next word will be CHASM.

Time is 2:20. Position of the hands: Hour hand at 2 (nearly).
Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees

11 How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?

A.5
B.6
C.7
D.None of these
Answer: Option BExplanation:
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.

12 One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
A.81 min.
B.108 min.
C.144 min.
D.192 min.
Answer: Option CExplanation:
Let the slower pipe alone fill the tank in x minutes.

13 A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
A 0%
B.5%
C.7.5%
D.10%
Answer: Option AExplanation:
C.P. = Rs. 3000.

15 David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
A.19
B.28
C.30
D.37
Answer: Option C